Equivalence Class

Tags

math

For an equivalence relation $R\subseteq A\times A$ the equivalence class of $a\in A$ with respect to $R$ is the set of elements related to $a$ by $R$. $$[a{]}_R=\{x\in A:aRx\}$$

Set of Equivalence Classes

For an equivalence relation $R$ the set of equivalence classes of $A$ with respect to $R$ is a partition of $A$.